The development of the interface tracking between two immiscible liquids
is one of the most challenging problems in fluid dynamics. The
simulation of the lubrication process, oil extraction, and the
physicochemical mechanism that govern the behavior of the uncertain
conduct of interface is a key element in “gas-oil” or “oil-water”
natural gas-oil reservoirs systems and should be tracked for optimal
recovery. Motivated by the interface evolution process, in this article,
an unsteady flow of two immiscible Eringen micropolar and
Dusty(fluid-particle suspension) fluids is considered through a
horizontal channel. The Analysis of the interface between two immiscible
Eringen micropolar and Dusty(fluid-particle suspension) fluids are
carried out. Although the channel wall is hyper-stick and no-slip, it is
believed that the fluid-fluid interface is unstable and can be also
deformed from one location to another; thus, the single momentum
equation is coupled for monitoring the interface profiles using the
VOF(Volume of fluid) technique. The modeled coupled- partial
differential equations are numerically solved by the modified B-spline
differential quadrature method. The interface profile under the
influence of different parameters, i.e. Froude, Capillary, wave and
Reynolds number, volume fraction function, the ratio of viscosities,
densities, and time is analyzed through the graph. It is noticed that
initially, the vertical elongation of the interface is large, and then
the shape of the interface (topology) evolves with time; hence the
undulating sequence occurs faster for a more considerable time and
eventually becomes stable. The qualitative characteristics of this flow
are sustained.